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Repulsive curves Posted: 30 Aug 2021 08:58 AM PDT Chris Yu, Henrik Schumacher, and Keenan Crane from Carnegie Mellon University are working on repulsive curves, which is a method to efficiently unravel curves so that they don’t overlap: Curves play a fundamental role across computer graphics, physical simulation, and mathematical visualization, yet most tools for curve design do nothing to prevent crossings or self-intersections. This paper develops efficient algorithms for (self-)repulsion of plane and space curves that are well-suited to problems in computational design. Our starting point is the so-called tangent-point energy, which provides an infinite barrier to self-intersection. In contrast to local collision detection strategies used in, e.g., physical simulation, this energy considers interactions between all pairs of points, and is hence useful for global shape optimization: local minima tend to be aesthetically pleasing, physically valid, and nicely distributed in space. Be sure to watch the video demo. Tags: curves, optimization, research

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